Determine whether the equation represents exponential growth, exponential decay, or neither. \( y=600(0.96)^{t} \)

The equation provided is: \[ y = 600 \times (0.96)^{t} \] To determine whether this represents **exponential growth**, **exponential decay**, or **neither**, we can analyze the components of the equation. ### General Form of Exponential Functions An exponential function can generally be written as: \[ y = y_0 \times a^{t} \] - **\( y_0 \)**: Initial value when \( t = 0 \) - **\( a \)**: Base of the exponential function - If **\( a > 1 \)**: The function represents **exponential growth** - If **\( 0 < a < 1 \)**: The function represents **exponential decay** - If **\( a = 1 \)**: The function remains **constant** ### Applying to the Given Equation In the equation \( y = 600 \times (0.96)^{t} \): - **Initial Value (\( y_0 \))**: 600 - **Base (\( a \))**: 0.96 Since the base \( a = 0.96 \) is **between 0 and 1** (\( 0 < 0.96 < 1 \)), this indicates that the function represents **exponential decay**. ### Interpretation As time \( t \) increases, \( (0.96)^{t} \) decreases because you are multiplying by a number less than 1 repeatedly. This causes the value of \( y \) to decrease over time, approaching zero but never actually reaching it. ### Conclusion The equation \( y = 600 \times (0.96)^{t} \) **represents exponential decay**.